ABSTRACT
To begin to make sense of what follows, think of the familiar quantities area and volume. These are associated with certain kinds of objects-planar regions or regions on surfaces, in the case of area; bodies in space, in the case of volume. The assignment of these quantities to appropriate objects is defined, and the definitions can be quite involved; in fact, the final chapter on the question of mere definitions of area and volume was perhaps not written until the twentieth century, with the introduction of Lebesgue measure.
